We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing network models that perfectly match the structure of some real scale-free networks, such as the Internet. We obtain an analytic solution, supported by extensive ...

In several applications, information is drawn from qualitative variables. In such cases, measures of central tendency and dispersion may be highly inappropriate. Variability for categorical data can be correctly quantified by the so-called diversity measures. These measures can be modified to quantify heterogeneity between groups (or subpopulations). Pinheiro et al. (2005) shows that Hamming di...

Let \((X, T^{1,0}X)\) be a compact connected orientable CR manifold of dimension \(2n+1\) with non-degenerate Levi curvature. Assume that X admits Lie group G action. Under certain natural assumptions about the action, we show G-invariant Szegő kernel for (0, q) forms is complex Fourier integral operator, smoothing away \(\mu ^{-1}(0)\) and there precise description singularity near ^{-1}(0)\),...

Consider the focusing 4D cubic wave equation∂ttu−Δu−u3=0,on(t,x)∈[0,∞)×R4. The main result states existence in energy space H˙1×L2 of multi-solitary waves where each traveling is generated by Lorentz transform from a specific excited state, with different but collinear speeds. state deduced non-degenerate sign-changing constructed Musso-Wei [34]. proof inspired techniques developed for 5D energ...

Following the success of using the null-field integral approach to determine the torsional rigidity of a circular bar with circular inhomogeneities (Chen and Lee in Comput Mech 44(2):221–232, 2009), an extension work to an elliptic bar containing elliptic inhomogeneities is done in this paper. For fully utilizing the elliptic geometry, the fundamental solutions are expanded into the degenerate ...

Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. In the present paper we establish some properties of integrating factors subjected to morphisms, and we...

We are interested in the feedback stabilization of a fluid flow over a flat plate, around a stationary solution, in the presence of perturbations. More precisely, we want to stabilize the laminarto-turbulent transition location of a fluid flow over a flat plate. For that we study the Algebraic Riccati Equation (A.R.E.) of a control problem in which the state equation is a doubly degenerate line...